This paper will begin by introducing several existing opinion dynamics models and
assessing their ability to represent empirical observations accurately. We will then
exclusively focus on the classic voter model and consider the effects of introducing a
small number of stubborn agents that can hold one of two different opinions. Stubborn
agents holding the same opinion are considered to belong to the same party and
to have directly opposing objectives to those belonging to the other party. Assuming
that each party’s objective is to maximize its expected number of supporters as
t → ∞, we will explore the optimal strategies for each party in both sequential and
simultaneous games. In the sequential case, we will propose the ‘convergence time
minimization’ strategy as a tractable proxy for the first mover’s optimal strategy and
assess its performance on network structures with varying degrees of homogeneity. In
the simultaneous case, we will seek to qualitatively understand the conditions under
which a pure strategy Nash equilibrium is expected to arise. Finally, we will explore
how the parties’ optimal strategies would change if the objective function were
adjusted so as to incorporate variance or if it were evaluated at a finite time horizon.
Our analysis and conclusions find applications in the commercial and political
fields, where a small number of entities seek to diffuse opposing beliefs through the
positioning of advertising resources.